Information granulation construction and representation strategies for classification in imbalanced data based on granular computing

Figures & data

Figure 1. IG construction strategy from majority class samples, minority class samples are preserved (Chen et al., 2008).

Figure 2. IG description: the concept of ‘sub-attributes’ used for numeric attribute (Chen et al., 2008).

Figure 3. IG construction strategy from sub-dataset corresponds to each class separately.

Figure 4. IG description: the concept of ‘sub-attributes’ (a) using for discretization of numeric attributes (number of discretized values is 10) and (b) for discrete attributes X_j (8 distinct values).

Table 1. An IG for versicolor class of iris dataset, discretized values with S_e = 5.

Condition attributes								Decision attribute (class)
Origin				After discretization
X1	X2	X3	X4
5.8	2.7	4.1	1	c	b	c	b	Versicolor
6.2	2.2	4.5	1.5	c	a	c	c	Versicolor
5.6	2.5	3.9	1.1	b	b	c	c	Versicolor
5.9	3.2	4.8	1.8	c	c	d	d	Versicolor

Note: represents discretized value of respectively (i = 1,2,3,4).

Table 2. The ranges of values of IG’s discretized attributes and sub-attributes representation correspondingly.

	Condition attributes				Decision attribute (class)
[min, max]	[b, c]	[a, c]	[c, d]	[b, d]	Versicolor
Sub-attributes	0 1 1 0 0	1 1 1 0 0	0 0 1 1 0	0 1 1 1 0	1

Note: Versicolor class is class one. Let 1 be the expected output value of neural networks when training the IG.

Table 3. Details of the experimental datasets.

Dataset	Title of data	Data size	Attributes + class	Attributes’ value		Class distribution
Wine	Wine	178	13 + 1	Continuous	13	Class 1	33.15%
	recognition					Class 2	39.89%
	data					Class 3	26.96%
Heart	Heart	270	13 + 1	Continuous	6	Class 1	55.56%
	disease			Discrete	3	Class 2	44.44%
	dataset			Binary	3
				Ordered	1
Vote	Vote	435	16 + 1	Discrete	16	Democrat	61.38%
						Republican	38.62%
Contraceptive	Contraceptive	1473	9 + 1	Continuous	2	No-use	43%
	method choice			Discrete	4	Long-term	23%
				Binary	3	Short-term	34%
Credit screening	Credit approval	653	15 + 1	Continuous	6	Unacceptable	45%
				Discrete	5	Acceptable	55%
				Binary	4
Pima	Pima-Indians-Diabetes	768	8 + 1	Continuous	8	Healthy	65%
						Diabetic	35%

Table 4. The experimental parameters for each dataset in Chen’s approach and our algorithm.

Dataset	S	H-index threshold	U-ratio threshold	Network structure	Iterations (NN)
Credit screening	5	0.73	0.05	(15..24)-29-1	20,000
Contraceptive	10	0.90	0.10	(9..18)-37-1	10,000
Wine	5	0.97	0.00	(13..22)-18-1	15,000
Pima	10	0.75	0.10	(8..17)-27-1	20,000
Heart	10	0.95	0.05	(13..22)-27-1	20,000
Vote	5	0.85	0.15	(16..25)-18-1	15,000

Table 5. Experimental results with accuracy for each class, overall accuracy, G-mean and mean squared error (MSE).

Dataset	Class	Proposed method (GrC on each class)				Chen’s method (GrC on the whole dataset)
		Accuracy – Mean (%)			MSE	Accuracy – Mean (%)			MSE
		Class accuracy	Overall accuracy	G-mean		Class accuracy	Overall accuracy	G-mean
Wine	Class 1	100	98.33	97.77	0.1817	98.33	97.74	96.59	0.1989
	Class 2	95.71				97.14
	Class 3	100				98.00
Heart	Class 1	91.33	91.48	91.38	0.29078	86.11	86.29	86.96	0.29554
	Class 2	91.66				88.33
Vote	Class 1	96.25	97.24	97.52	0.18290	95.69	96.31	96.85	0.18316
	Class 2	98.82				98.14
Credit	Unacceptable	83.83	85.14	84.73	0.29403	81.77	87.95	78.55	0.26794
screening	Acceptable	86.22				85.57
Contraceptive	No-use	14.30	35.02	16.62	0.89522	16.17	35.89	7.66	0.89373
	Long-term	57.10				30.95
	Short-term	46.09				44.39
Pima	Healthy	78.00	73.10	71.05	0.3916	84.48	74.02	59.64	0.31875
	Diabetic	66.66				42.10
Average		79.00	80.05	76.51	0.37	74.80	79.70	71.04	0.36
Standard deviation		25.03	23.93	30.98	0.27	28.41	23.08	33.99	0.27

Note: Bold values are the best results of each experimental kind.

Table 6. The computational time.

Dataset	Our method (s)	Chen’s method (s)
Credit screening	59 . 5	118
Contraceptive	119.5	423.87
Wine	12.5	21.5
Pima	56.5	65.5
Heart	22.32	66
Vote	22.43	27.09
Average	48.79	120.32
Standard deviation	39.71	152.68

Note: Bold values are the best results of each experimental kind.

Chen, M.-C., Chen, L.-S., Hsu, C.-C., & Zeng, W.-R. (2008). An information granulation based data mining approach for classifying imbalanced data. Information Sciences, 178(16), 3214–3227. doi: 10.1016/j.ins.2008.03.018

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